Posted by **Anonymous** on Wednesday, January 28, 2009 at 3:49pm.

I find it difficult to take the derivative of something that has a constant base with a variable as an exponent...and simplify it... PLEASE HELP ME!

f(x) = e^(x^(-1))

f'(x) = -1(e^(x^(-2))e^(x^(-1))

f'(x) = -e^(x^(-2))e^(x^(-1))

?????

and... f(x) = 3^x

f'(x) = 3^x

- Math - Derivatives -
**Damon**, Wednesday, January 28, 2009 at 4:22pm
d/dx e^u = e^u du/dx

here u = x^-1

du/dx = -1 x^-2

so

d/dx e^(x^-1) = -x^-2 e^(x^-1)

= -(1/x^2)e^(1/x^2)

Try the others using that recipe:

d/dx e^u = e^u du/dx

- Math - Derivatives -
**Anonymous**, Wednesday, January 28, 2009 at 4:34pm
WOW that actually helps a lot and less confusing to solve! Thanks so much!

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